Related papers: Speed limits and locality in many-body quantum dyn…
As experiments are increasingly able to probe the quantum dynamics of systems with many degrees of freedom, it is interesting to probe fundamental bounds on the dynamics of quantum information. We elaborate on the relationship between one…
The attempt to gain a theoretical understanding of the concept of time in quantum mechanics has triggered significant progress towards the search for faster and more efficient quantum technologies. One of such advances consists in the…
A long standing open problem whether a heat engine with finite power achieves the Carnot efficiency is investigated. We rigorously prove a general trade-off inequality on thermodynamic efficiency and time interval of a cyclic process with…
In this thesis we present new results relevant to two important problems in quantum information science: the development of a theory of entanglement and the exploration of the use of controlled quantum systems to the simulation of quantum…
We review recent results on many-body localization for two explicitly analyzable models of many-body quantum systems, the XY spin chain in transversal magnetic field as well as interacting systems of harmonic quantum oscillators. In both…
We prove that quantum information propagates with a finite velocity in any model of interacting bosons whose (possibly time-dependent) Hamiltonian contains spatially local single-boson hopping terms along with arbitrary local…
We introduce the notion of transmission time to study the dynamics of disordered quantum spin chains and prove results relating its behavior to many-body localization properties. We also study two versions of the so-called Local Integrals…
We supply the mathematical arguments required to complete the proofs of two previously published results: Lieb-Robinson bounds for the dynamics of quantum lattice systems with unbounded on-site terms in the Hamiltonian and the existence of…
We give an introduction into some aspects of the emerging mathematical theory of many-body localization (MBL) for disordered quantum spin chains. In particular, we discuss manifestations of MBL such as zero-velocity Lieb-Robinson bounds,…
How fast can correlations spread in a quantum many-body system? Based on the seminal work by Lieb and Robinson, it has recently been shown that several interacting many-body systems exhibit an effective light cone that bounds the…
Many-body localization was proven under realistic assumptions by constructing a quasi-local unitary rotation that diagonalizes the Hamiltonian (Imbrie, 2016). A natural generalization is to consider all unitaries that have a similar…
Quantum speed limit is bound on the minimum time a quantum system requires to evolve from an initial state to final state under a given dynamical process. It sheds light on how fast a desired state transformation can take place which is…
We prove that the time required for sustained information scrambling in any Hamiltonian quantum system is universally at least logarithmic in the entanglement entropy of scrambled states. This addresses two foundational problems in…
Many-body localization, the persistence against electron-electron interactions of the localization of states with non-zero excitation energy density, poses a challenge to current methods of theoretical and numerical analysis. Numerical…
We show that, assuming that quantum mechanics holds locally, the finite speed of information is the principle that limits all possible correlations between distant parties to be quantum mechanical as well. Local quantum mechanics means that…
What is the minimal time until a quantum system can exhibit genuine quantum features? To answer this question we derive quantum speed limits for two-time correlation functions arising from statistics of measurements. Generally, these…
We study the quantum dynamics generated by Bose-Hubbard Hamiltonians with long-ranged (power law) terms. We prove two ballistic propagation bounds for suitable initial states: (i) A bound on all moments of the local particle number for all…
Many-body quantum systems typically display fast dynamics and ballistic spreading of information. Here we address the open problem of how slow the dynamics can be after a generic breaking of integrability by local interactions. We develop a…
Quantum speed limits (QSLs) provide an upper bound for the speed of evolution of quantum states in any physical process. Based on the Stratonovich-Weyl correspondence, we derive a universal QSL bound in arbitrary phase spaces that is…
We consider the dynamics of the Bose-Hubbard model on general lattices and prove a Lieb-Robinson bound for observables whose supports are separated by an initially almost particle-free region. We further obtain a maximal velocity bound for…